A review of Dark Matter and Dark Energy

Introduction
Many observations, and subsequent cosmological theories, have found that
approximately 95% of the mass and energy in the universe is dark and in-
visible, the true nature of which is largely unknown. The matter component
is known as dark matter (DM) and the energy component dark energy (DE)
This is a brief review of the history and current status of DM and DE.

Dark Matter
DM has a surprisingly long and interesting history. In 1933, the renowned
astrophysicist, Fritz Zwicky published a paper on the velocity dispersion of
galaxies within the Coma cluster. He found that the velocity dispersion of
galaxies within the cluster was so high that in order for the system to remain
stable there must be some “missing mass” i.e. mass which is not detectable
optically. Further research in this area continued but it wasn’t until the
1970s when astronomers began accurately measuring the rotation curves of
spiral galaxies, with the discovery of HI 21cm radio emission, that interest in
this area became of great importance. HI 21cm radio emission is produced
by neutral hydrogen during a change of energy state. It has a very precise
wavelength of 21cm. Rotation curves are a measure of the orbital velocity of
the stars and gas in a galaxy plotted as a function of distance from the galactic
centre. According to Keplerian laws rotation curves would be expected to
decline with increasing radius however it was found that they remain flat i.e.
constant, all the way out to the largest radii observed, both optically and
with 21 cm. According to Newtonian gravity this implies that there must
be some “hidden mass” within the galaxies exerting a gravitational effect on
the system resulting in these flat rotation curves. This “hidden mass” was
termed dark matter.
Figure 1: Examples of flat galaxy rotation curves (Ruben, 1979)
Apart from high velocity dispersions in galaxy clusters and flat rota-
tion curves other evidence for DM includes gravitational lensing, hot gas in
clusters, the Cosmic Microwave Background (CMB) and through computer
modelling of the growth of large scale structure in the early universe (dis-
cussed later). Gravitational lensing occurs when light from distant galaxies
behind a galaxy cluster is distorted due to the large gravitational pull of the
cluster. This is known as strong lensing and is quite rare, however weak
lensing also occurs where there is just a small distortion of the galaxies size
and shape. The mass of the galaxy cluster can be measured and compared
to how much the light is expected to be bent by gravity. The results show
that there must be far more mass in clusters than can be detected. Galaxy
clusters when viewed in X-ray reveal huge amounts of hot gas which can only
be explained by large amounts of DM which provide a potential gravitational
well to hold the gas. The CMB is the remnants of radiation from the early
universe. Anisotropies in the CMB also reveal evidence for DM. Anisotropies
are irregularities seen in the CMB which, after having been thoroughly stud-
ied, reveal what would be expected if thermal variations in a small space
had grown to form the observable universe today. Before decoupling from
baryonic matter (i.e. ordinary matter comprised of mainly protons and neu-
trons), photons underwent oscillations that froze in at redshift z ≈ 1100.
Decoupling refers to events in the early universe when different particles fall
out of thermal equilibrium with each other. By studying the height of the
peaks in these oscillations it has been found that the universe is comprised of
approximately 5% baryonic matter, 26% dark matter and the remainder dark
energy (discussed later). Some authors (Freese, 2017) regard the evidence of
DM from the CMB as “irrefutable”.
Further evidence of DM, which has been described as “direct empirical
proof” (Clowe et al, 2006), has been found in observations of the Bullet clus-
ter of galaxies. The Chandra X-ray observatory has detected the baryonic
matter in the merger of two smaller clusters, whilst DM has been deduced
from gravitational lensing, and they clearly show that are behaving differ-
ently. At the collision point the baryonic matter has slowed down due to
friction whilst the DM has passed through this point.
Figure 2: The bullet cluster: a) Optical view from Magellan telescope with
plotted contours of mass distribution obtained from gravitational lensing. b)
Same contours but with Chandra X-ray data showing hot plasma. Most of
the matter is lying in a different location to the hot plasma which has been
slowed down by friction during the merger. (Clowe et al, 2006)
With the growing evidence for the existence of DM, obvious questions to
ask are “What is it made of?” and “Is it baryonic?”. About twenty years
ago it was suggested that dark matter is comprised of objects such as faint
stars, sub-stellar objects or stellar remnants. Collectively these came to be
known as massive compact halo objects (MACHOs). However recent studies
(Freese, 2017) have found that these objects couldn’t account for all the DM
in the universe. This then suggests that if DM exists it must be non-baryonic.
Particle physicists have postulated many possible candidates for non-
baryonic DM particles. These include neutrinos, primordial black holes
(PBHs), magnetic monopoles, neutalinos and photinos. However, many of
these have been effectively ruled out by research e.g. Gaggero et al (2016)
who concluded that PBHs couldn’t account for more than 20% of DM in the
universe. Two of the most popular non-baryonic DM candidates currently
are: Axions and Weakly Interacting Massive Particles (WIMPs). These are
both hypothetical particles invented by particle physicists for other reasons
than DM, which relieves cosmologists of having to invent new particles. Ax-
ions arise from a problem in quantum chromodynamics but have interesting
consequences for cosmology as they are predicted to be stable over cosmolog-
ical timescales (Bertone and Hooper, 2016) and could therefore theoretically
constitute DM. WIMPs have been the source of many theoretical studies of
DM and are now considered to be the leading class of DM particles, partly
because they are predicted to interact via gravity and have a large mass
compared to other particles.
There are currently four main approaches to discovering WIMPs. There
are ongoing experiments, with ever increasing sensitivity, at CERN, using
the Large Hadron Collider. One of the goals of the two detectors, ATLAS
and CMS, was specifically to try and discover the nature of DM. It has so
far been unsuccessful in that respect. There are also attempts to directly
detect WIMPs in underground DM laboratories worldwide. So far there has
been no confirmed detection of WIMPs. Indirect detection of WIMPs is also
being carried out in objects such as the galactic centre, galaxy clusters and
dwarf galaxies i.e. objects with a predicted over-density of WIMPs. Again,
there has been no confirmed detection.
An interesting fourth approach to the hunt for DM is to discover dark
stars. It is predicted that the first stars to form in the early universe, at
redshift z ≈ 10 − 50, may have been comprised of mainly hydrogen and
helium and yet were powered by DM heating rather than nuclear fusion.
These are believed to have formed when the universe was much denser than
now and consisted of high density DM halos. It is hoped that the James
Webb Space Telescope will be able to detect dark stars and so enable us to
study WIMPs in more detail.
With the advent of numerical simulations, models that involve DM have
been extensively explored. Currently a very popular model of the evolution of
structure in the universe is the Lambda Cold Dark Matter (ΛCDM ) model.
Λ here refers to the cosmological constant discussed in the DE section. Com-
puter simulations have shown that if the DM particles are relativistic (“hot”)
then, on small scales, density fluctuations are Silk damped, or washed out,
the random thermal motion of DM particles. This results in small scale struc-
ture fluctuations to be suppressed. However, if the DM particles are “cold”
i.e. cold dark matter (CDM), then they undergo a very different structure
formation because they have a much smaller free-streaming length and can
form low mass halos which can gradually build up into larger DM structures.
These DM structures provide a gravitational well that baryonic particles can
fall into to form baryonic structure. This results in a bottom-up process of
structure formation which is very different to the top-down sequence pre-
dicted for hot DM. These simulations have further convinced cosmologists
that CDM comprised of WIMPs are the best explanation for the growth of
large scale structure in the universe. In fact, the ΛCDM model agrees so
well with observations that it is often regarded as the “standard model of
cosmology”.
Even though the evidence for DM is growing, there has been no confirmed
detection of DM or WIMPs and the theory of DM leads to a number of
problems (Sellwood and Kosowsky, 2000) which I don’t have space to detail
here. This has led some cosmologists to believe that the Newtonian theory
of gravity may need to be amended. One of these theories is called Modified
Newtonian Dynamics (MOND). It is a conceptually simple idea but it has
some far-reaching consequences. The basic idea is that Newton’s second
law be amended from F = ma to F = ma2/a0 in the limit of very low
accelerations (a << a0 ≈ 1.2 × 10−10m/s2). This could then account for
the observed motions of stars within galaxies without having to introduce
DM. MOND has been quite successful with explaining flat rotation curves
but less successful with galaxy clusters. MOND, however, is not without its
own problems particularly when it comes to integrating MOND with general
relativity (GR), explaining the growth of large scale structure, and explaining
the first CMB acoustic peak. It would appear that either the LHC, or any
detection methods previously described, will eventually detect WIMPs and
confirm the existence of DM and MOND will die out as a theory or, if no
detection of DM is forthcoming then the theory of MOND may well grow.

Dark Energy
Cosmic acceleration, and associated DE, is arguably one of the greatest un-
solved problems in contemporary physics. DE actually has a longer history
than DM. As Einstein was forming his field equations for general relativity he
realised that this would result in a universe that would gravitationally attract
and therefore contract. He therefore introduced the cosmological constant
to balance gravity and ensure a static universe. When observations by Hub-
ble in 1929 revealed that the universe is expanding, Einstein referred to his
failure to predict a dynamic universe has his biggest blunder. The cosmo-
logical constant therefore fell into disuse. However, in 1980 Alan Guth and
Alexei Starobinsky proposed the idea of cosmic inflation which involved an
exponential expansion of the universe immediately after the Big Bang. The
theory of inflation involves a negative pressure field which creates a repulsive
force. This idea is similar to DE, however even when inflation became widely
accepted the cosmological constant was considered irrelevant. This changed
however in 1998 when observations of supernovae revealed that the universal
expansion is accelerating. This was the first direct evidence of DE.
Type Ia supernovae occur when a white dwarf in a binary pair accretes
enough mass so that it goes over the Chandrasekhar mass and triggers a
supernova. The supernova therefore doesn’t depend on the mass of the white
dwarf on the other star in the binary. Type Ia supernovae can be considered
as standard candles and enable astronomers to obtain a luminosity distance.
To measure cosmic expansion the apparent magnitude of distant supernovae
are compared to those of more local supernovae which are not affected by
DE. The Supernova Cosmology Project which carried out one of the surveys
in 1998 found that, with a flat cosmology (ΩΛ + Ωm = 1), that Ωm = .28
and so that ΩΛ = .72. Ω is the density parameter and is defined as the ratio
of the observed density to the critical density. Ωm here is the proportion of
matter in universe (DM and baryonic) whilst ΩΛ represents the proportion
of DE in universe. The deceleration parameter is calculated as follows:
2(Ωm − 2ΩΛ + 2ΩR) (1)
This then results in a negative deceleration parameter indicating that the
expansion of the universe is accelerating. Since 1998 there have been many
more supernova surveys and it is has become an active area of observational
cosmology. All this supernova data indicates that the apparent luminosity
of Type Ia supernovae declines more rapidly with increasing redshift than
would be expected if ΩM = 1 and ΩΛ = 0 i.e. an Einstein-de Sitter universe,
or the luminosity distance is greater than expected. Of course, these data
could be interpreted as being due to other effects such as dust or gas in the
line of sight. More evidence is required.
Although it doesn’t directly constrain DE, data obtained from CMB
anisotropies does provide accurate figures for parameters that are needed
in order to study DE. By measuring anisotropies within the CMB data, from
WMAP and Planck satellites, accurate figures for ΩB and ΩDM have been
obtained.
Figure 3: The Planck satellite helped provide accurate figures for cosmolog-
ical parameters (ESA , 2013)
Similarly, Baryonic Acoustic Oscillations (BAO) also help the study of
DE by constraining cosmological parameters. BAOs are regular and periodic
fluctuations in the density of baryonic matter. They are measured by looking
at large scale structures in the universe through galaxy surveys. In a similar
way that Type Ia supernovae are standard candles, BAOs are standard rulers.
By comparing the clustering of galaxies today (using redshift surveys like
the Sloan Digital Sky Survey - SDSS) and comparing it with data from
CMB cosmologists have a way of measuring DE that is independent of the
supernova method.
Unlike DM, where particle physicists and cosmologists have established
theories as to what it may be comprised of, the nature of DE is completely
unknown. DE is often referred to as vacuum energy. According to quantum
field theory a vacuum or empty space actually consists of transient fluctua-
tions known as virtual particles. They do, however, have some properties in
common with “ordinary” particles. It has been suggested that these virtual
particles may give rise to DE. However, the density of virtual particles is
about 120 times larger than the DE density. There is currently no explana-
tion for this. The DE density is believed to be ≈ 10−27kg/m3 which is low
but it has such a profound effect on the universe because it fills all of empty
space.
There are many theories for DE. However, the simplest one is that it
is constant i.e. a cosmological constant. The cosmological constant has
a negative pressure equal to its energy density and so exerts a repulsive
force causing the expansion of the universe to accelerate i.e. P = −ρ. The
previously mentioned ΛCDM model uses this form of DE and is the currently
preferred cosmological model. An important parameter in the study of DE
is the equation of state parameter ω. This comes from:
P = ωρc2 (2)
where P is pressure, ρ is density, c is speed of light and ω is the equation of
state parameter. In the ΛCDM model ω is assumed to be -1.
Another theory of DE is quintessence. In this theory, DE is assumed to
be a scalar field and unlike the cosmological constant can vary in time and
space. However, there is currently no evidence to support this theory. It has
been suggested that instead of vacuum energy, cosmic acceleration can be
explained by a modified version of GR. Tests of GR within the solar system
have proven the theory to be accurate but it may be the case that GR breaks
down on cosmological scales. However there currently is no viable theory of
GR that can fully explain cosmic acceleration without introducing some form
of DE. However, this doesn’t preclude a theory arising in the future as, for
example, it wasn’t until the advent of GR in 1915 that the precession of
Mercury’s orbit could be fully explained.
The Dark Energy Survey (DES) was specifically created to probe DE.
Using a wide-field camera on the 4m Blanco Telescope in Chile the project
aims to catalogue 300 million galaxies. The main goals of the survey are to
characterise DE and DM and also to test alternative theories of gravity. The
survey takes photometric redshifts of galaxies and also carries out galaxy-
galaxy weak lensing measurements i.e. where both the lenses and sources
are galaxies. It is also carrying out a time domain survey of Type Ia su-
pernovae. Last year the project reported that they had further constrained
Ωm to be = 0.31 ± 0.09. The SDSS is also carrying out DE probes with the
Extended Baryon Oscillation Spectroscopic Survey (eBOSS). The main goals
of eBOSS are to measure clustering on large scales and to measure BAOs.
Other projects include Panoramic Survey Telescope and Rapid Response
System (Pan-STARRS) and the Hobby-Eberly Telescope Dark Energy Ex-
periment (HETDEX). One of the aims of Pan-STARRS was to constrain the
equation of state parameter for DE (ω) which was found to be ω = −1.14
(Zheng et al, 2014). The Hobby-Eberly Telescope has recently been upgraded
for HETDEX and will probe DE through spectrographs of galaxies over the
redshift 0 < z < 4 and also analysing BAOs. The aim of HETDEX is to
provide a direct detection of DE at z ≈ 3 (Hill et al, 2008).
A new and exciting development by the European Space Agency, which
will further probe DE, will be the launch of Euclid which is expected to be in
2020. Euclid aims to find out the nature the acceleration of the expansion of
the universe and DE. It will measure shapes and redshifts of galaxies and also
explore the large-scale structure of the universe by measuring the distribution
of galaxy clusters. Euclid is a satellite equipped with a 1.2m telescope and
three imaging and spectroscopic instruments working in optical and near-
infrared. It will be placed at the L2 Langrange point, a stable point in space,
and is planned to operate for six years. The plan is cover 15000 square
degrees of sky and image one billion galaxies and take redshifts measurements
of 100,000 galaxies (Amendola et al, 2016). With these data Euclid will able
to detail clustering of galaxies out to redshift z=2 and out to redshift z=3
utilising weak lensing. Redshift measurements and weak lensing will also
be accompanied by measuring correlations with the CMB, obtaining galaxy
cluster information, strong lensing and possibly even obtaining luminosity
distance through supernovae Type Ia measurements.
DE may well have a profound effect on the final fate of the universe. Ob-
servations suggest that the expansion of the universe will continue to acceler-
ate forever and so the universe will cool as it expands. Redshift will eventu-
ally stretch photons to undetectable wavelengths and galaxies will therefore
appear to disappear. Star formation will cease as gas supply runs out. Stars
will eventually die out, one by one, leaving stellar remnants. Some theories
even predict that stellar remnants will disappear due to proton decay leaving
only black holes, which themselves will eventually disappear due to Hawking
radiation. Proton decay is a hypothetical form of radioactive decay in which
protons decay into lighter particles. Hawking radiation is blackbody radia-
tion believed to be emitted by black holes because of quantum effects near
the event horizon. This is often referred to as the heat death of the universe.
It would seem that the ultimate fate of our universe could potentially be a
very cold, dark void.

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Howard Kinsman
May 5, 2017